Is there a way to "lean" hairs without combing?
You'll want to be doing something with the tangents.

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TL;DR Enable Advanced, set 'Rot' to 0.5 and play with the Normal and Tangent values.

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You'll need to enable Advanced in the hair options:


Then go to the 'Velocity' section, under 'Emitter Geometry.' The 'Normal' value is set to the length of the hair divided by four. (Just don't ask me why.) Increase the Tangent value to something like 0.1, increasing the influence of the tangent on the length of the hair. (Those strands on the side are doing their own thing; that's lazy modelling on my part and should not happen.)


Then modify the Rot attribute (Tangent rotation) to 0.5 to make the particles rotate in the direction you wanted. If you wanted you could change it to another value to make the hair rotate in a different direction. Just play with it for the effect you want.


The 'Rot' parameter is basically rotating the tangent around the normal, with -1 to 1 mapped to -180 to 180 degrees. This makes sense if you imagine that there are two imaginary lines for every hair (in this case, on every face.) The red is the normal and the blue is the tangent. The hair is being pulled in both directions at once, so its length outwards is the Normal value (0.075) and its length sideways is the Tangent value (0.8). The diagram is nowhere near to scale.


If you want to change the rotation side-to-side of the hair you will have to do a bit of fiddling with the Normal and Tangent values, but not the Rot. Because of the way the Tangent and Normals work (as I explained above), we can do a little trigonometry to find the length and direction of the final strand. In particular, with a Rot value of 0.5, if the Normal value is n and the Tangent value is t:


the length of the final hair strand will be sqrt(n^2 + t^2) (Pythagoras)
the rotation of the final hair strand side-to-side will be arcsin(n/t).


(arcsin is the inverse sin function.)